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Simplifying 1.7x2 + -6x + -21 = 0 Reorder the terms: -21 + -6x + 1.7x2 = 0 Solving -21 + -6x + 1.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.7 the coefficient of the squared term: Divide each side by '1.7'. -12.35294118 + -3.529411765x + x2 = 0 Move the constant term to the right: Add '12.35294118' to each side of the equation. -12.35294118 + -3.529411765x + 12.35294118 + x2 = 0 + 12.35294118 Reorder the terms: -12.35294118 + 12.35294118 + -3.529411765x + x2 = 0 + 12.35294118 Combine like terms: -12.35294118 + 12.35294118 = 0.00000000 0.00000000 + -3.529411765x + x2 = 0 + 12.35294118 -3.529411765x + x2 = 0 + 12.35294118 Combine like terms: 0 + 12.35294118 = 12.35294118 -3.529411765x + x2 = 12.35294118 The x term is -3.529411765x. Take half its coefficient (-1.764705883). Square it (3.114186853) and add it to both sides. Add '3.114186853' to each side of the equation. -3.529411765x + 3.114186853 + x2 = 12.35294118 + 3.114186853 Reorder the terms: 3.114186853 + -3.529411765x + x2 = 12.35294118 + 3.114186853 Combine like terms: 12.35294118 + 3.114186853 = 15.467128033 3.114186853 + -3.529411765x + x2 = 15.467128033 Factor a perfect square on the left side: (x + -1.764705883)(x + -1.764705883) = 15.467128033 Calculate the square root of the right side: 3.932826977 Break this problem into two subproblems by setting (x + -1.764705883) equal to 3.932826977 and -3.932826977.Subproblem 1
x + -1.764705883 = 3.932826977 Simplifying x + -1.764705883 = 3.932826977 Reorder the terms: -1.764705883 + x = 3.932826977 Solving -1.764705883 + x = 3.932826977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.764705883' to each side of the equation. -1.764705883 + 1.764705883 + x = 3.932826977 + 1.764705883 Combine like terms: -1.764705883 + 1.764705883 = 0.000000000 0.000000000 + x = 3.932826977 + 1.764705883 x = 3.932826977 + 1.764705883 Combine like terms: 3.932826977 + 1.764705883 = 5.69753286 x = 5.69753286 Simplifying x = 5.69753286Subproblem 2
x + -1.764705883 = -3.932826977 Simplifying x + -1.764705883 = -3.932826977 Reorder the terms: -1.764705883 + x = -3.932826977 Solving -1.764705883 + x = -3.932826977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.764705883' to each side of the equation. -1.764705883 + 1.764705883 + x = -3.932826977 + 1.764705883 Combine like terms: -1.764705883 + 1.764705883 = 0.000000000 0.000000000 + x = -3.932826977 + 1.764705883 x = -3.932826977 + 1.764705883 Combine like terms: -3.932826977 + 1.764705883 = -2.168121094 x = -2.168121094 Simplifying x = -2.168121094Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.69753286, -2.168121094}
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